End of Course Specifications: Benchmarks
MA.912.D: Discrete Mathematics
MA.912.D.6: Develop an understanding of the fundamentals of propositional logic, arguments, and methods of proof.
MA.912.D.6.2: Find the converse, inverse, and contrapositive of a statement.
MA.912.D.6.3: Determine whether two propositions are logically equivalent.
MA.912.D.6.4: Use methods of direct and indirect proof and determine whether a short proof is logically valid.
MA.912.G.1: Understand geometric concepts, applications, and their representations with coordinate systems. Find lengths and midpoints of line segments, slopes, parallel and perpendicular lines, and equations of lines. Using a compass and straightedge, patty paper, a drawing program or other techniques, students also construct lines and angles, explaining and justifying the processes used.
MA.912.G.1.3: Identify and use the relationships between special pairs of angles formed by parallel lines and transversals.
MA.912.G.2: Identify and describe polygons (triangles, quadrilaterals, pentagons, hexagons, etc.), using terms such as regular, convex, and concave. Find measures of angles, sides, perimeters, and areas of polygons, justifying the methods used. Apply transformations to polygons. Relate geometry to algebra by using coordinate geometry to determine transformations. Use algebraic reasoning to determine congruence, similarity, and symmetry. Create and verify tessellations of the plane using polygons.
MA.912.G.2.1: Identify and describe convex, concave, regular, and irregular polygons.
MA.912.G.2.3: Use properties of congruent and similar polygons to solve mathematical or real-world problems.
MA.912.G.2.4: Apply transformations (translations, reflections, rotations, dilations, and scale factors) to polygons to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tessellations of the plane using polygons.
MA.912.G.2.5: Explain the derivation and apply formulas for perimeter and area of polygons (triangles, quadrilaterals, pentagons, etc.).
MA.912.G.2.7: Determine how changes in dimensions affect the perimeter and area of common geometric figures.
MA.912.G.3: Classify and understand relationships among quadrilaterals (rectangle, parallelogram, kite, etc.). Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas, and prove theorems involving quadrilaterals
MA.912.G.3.1: Describe, classify, and compare relationships among quadrilaterals including the square, rectangle, rhombus, parallelogram, trapezoid, and kite.
MA.912.G.3.2: Compare and contrast special quadrilaterals on the basis of their properties.
MA.912.G.3.4: Prove theorems involving quadrilaterals.
MA.912.G.4: Identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.). Define and construct altitudes, medians, and bisectors, and triangles congruent to given triangles. Prove that triangles are congruent or similar and use properties of these triangles to solve problems involving lengths and areas. Relate geometry to algebra by using coordinate geometry to determine regularity, congruence, and similarity. Understand and apply the inequality theorems of triangles.
MA.912.G.4.1: Classify, construct, and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.
MA.912.G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, perpendicular bisectors, orthocenter, centroid, incenter, and circumcenter.
MA.912.G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and areas.
MA.912.G.4.6: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.
MA.912.G.4.7: Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge Theorem.
MA.912.G.5: Apply the Pythagorean Theorem to solving problems, including those involving the altitudes of right triangles and triangles with special angle relationships. Use special right triangles to solve problems using the properties of triangles.
MA.912.G.5.1: Prove and apply the Pythagorean Theorem and its converse.
MA.912.G.5.2: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.
MA.912.G.5.3: Use special right triangles (30° - 60°- 90° and 45° - 45°- 90°) to solve problems.
MA.912.G.5.4: Solve real-world problems involving right triangles.
MA.912.G.6: Define and understand ideas related to circles (radius, tangent, chord, etc.). Perform constructions, and prove theorems related to circles. Find measures of arcs and angles related to them, as well as measures of circumference and area. Relate geometry to algebra by finding the equation of a circle in the coordinate plane.
MA.912.G.6.2: Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.
MA.912.G.6.4: Determine and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).
MA.912.G.6.6: Given the center and the radius, find the equation of a circle in the coordinate plane or given the equation of a circle in center-radius form, state the center and the radius of the circle.
MA.912.G.6.7: Given the equation of a circle in center-radius form or given the center and the radius of a circle, sketch the graph of the circle.
MA.912.G.7: Describe and make regular and nonregular polyhedra (cube, pyramid, tetrahedron, octahedron, etc.). Explore relationships among the faces, edges, and vertices of polyhedra. Describe sets of points on spheres, using terms such as great circle. Describe symmetries of solids, and understand the properties of congruent and similar solids.
MA.912.G.7.5: Explain and use formulas for lateral area, surface area, and volume of solids.
MA.912.G.7.7: Determine how changes in dimensions affect the surface area and volume of common geometric solids.
MA.912.G.8: In a general sense, mathematics is problem solving. In all mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results. At this level, apply these skills to making conjectures, using axioms and theorems, constructing logical arguments, and writing geometric proofs. Learn about inductive and deductive reasoning and how to use counterexamples to show that a general statement is false.
MA.912.G.8.2: Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.
MA.912.T.2: Understand how the trigonometric functions relate to right triangles, and solve word problems involving right and oblique triangles. Understand and apply the laws of sines and cosines. Use trigonometry to find the area of triangles.
MA.912.T.2.1: Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) in terms of angles of right triangles.
Correlation last revised: 9/16/2020